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Proof step 18 from proof transitivity (previous step)

i0 * j * j1 < i1 * j0 * j, i * j0 * j1 < i0 * j * j1, i * j0 < i0 * j, 0 < j0, 0 < j, i0 * j1 < i1 * j0, j * i1 ≤ i * j1, 0 < j1 ⊦ i * j0 * j1 < i1 * j0 * j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < j ∧ j < j0 → i < j0 subst: [i, j, j0] → [i * j0 * j1, i0 * j * j1, i1 * j0 * j] rotate: F spec: int-basic1 inst: name: trans-01

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i * j0 * j1, i0 * j * j1, i1 * j0 * j